no part of the password overlaps each other

there is no math involved

If you can read it without decoding it, you probably should

there are four letters and then 7 numbers

Double digit numbers count as one number out of the 7 you need.

You obtained the first card you need in your invitation. Alys has no match.

x/19 denotes numbers in a set.

The manticore is already near the moth

context clues can match many of the cards without needing to translate the tapestries.